Abstract
Optical surface scattering analyses based on diffractive optics (DO) are typically applied to one surface; however, there is a need for simulating surface scattering losses for devices having many surface interactions such as light pipes. Light pipes are often simulated with geometric optics (GO) using ray tracing, where surface scattering is driven by the surface slope distribution. In the DO case, surface scattering analyses depend on the spatial frequency distribution and amplitude as well as wavelength, with the sinusoidal grating as a fundamental basis. A better understanding of the link, or transition, between DO and GO scattering domains would be helpful for efficiently incorporating scattering loss analyses into ray trace simulations. A formula for the root-mean-square (rms) scattered angle width of a sinusoidal reflection grating that depends only on the surface rms slope is derived from the nonparaxial scalar diffraction theory, thereby linking it to GO. The scatter angle’s mean and rms width are evaluated over a range of grating amplitudes and periods using scalar theory and full vector simulations from the COMSOL® wave optic module for a sinusoidal reflection grating. The conditions under which the diffraction-based solution closely approximates the GO solution, as predicted by the rms slope, are identified. Close agreement is shown between the DO and GO solutions for the same surface rms slope scattering loss due to angular filtering near the critical angle of a total internal reflection (TIR) glass-to-air interface.
Highlights
Optical surface scattering analyses based on diffractive optics (DO) are typically applied to one surface; there is a need for simulating surface scattering losses for devices having many surface interactions such as light pipes
The light is guided via total internal reflection as it propagates along the light pipe and undergoes numerous sidewall reflections that vary in number depending on the incident ray angles
Both criteria converge to this result; smooth surface scattering is typically discussed in the DO domain without comment on the relevance for a geometrical optics approximations (GOA) solution
Summary
Optical surface scattering analyses are often conducted using a diffraction-based. C. Beyond the GO simulation, the step is to evaluate the potential for diffraction-based scattering effects that could introduce wavelength-dependent losses in the light pipe. For large values of σ, for example σ ≥ 0.3λ [4], the DO solutions for the scattered angle distribution are proportional to the rms slope, so the DO and GO solutions are driven by the same surface property. A larger range of applicability for the GO solution was proposed by Tang [5], who defined a criterion for the rms roughness, σ cosθ0 ≥ 0.17λ , whereby the scattered light distribution from the GO solution compares closely with a full wave solution. Little attention is typically given to the dependence on angle of incidence with respect to when diffractive effects are negligible and surface scattering can be adequately approximated with a GOA. The necessary approximations and simulation results to evaluate the applicability over a range of amplitudes and grating periods from low- to mid-spatial periods are the focus of the remaining sections
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